KABUL, Afghanistan — The United States is considering slowing its military exit from Afghanistan by keeping a larger-than-planned troop presence this year and next because the new Afghan government is proving to be a more reliable partner, U.S. Defense Secretary Ash Carter said Saturday.

Carter, on his first overseas trip since starting the Pentagon job Tuesday, also said the Obama administration is “rethinking” the counterterrorism mission in Afghanistan, although he did not elaborate.

No decisions have been made, but President Barack Obama will discuss a range of options for slowing the U.S. military withdrawal when Afghan president Ashraf Ghani visits the White House next month, Carter said at a news conference with Ghani. The presidents also plan to talk about the future of the counterterrorism fight in Afghanistan, he said.

Carter did not say Obama was considering keeping U.S. troops in Afghanistan beyond 2016, only that the president was rethinking the pace of troop withdrawals for 2015 and 2016.

There are about 10,000 U.S. troops in Afghanistan, down from a peak of 100,000 as recently as 2010-11.

While the White House recently acknowledged it was reconsidering the exit plan, Carter’s remarks were the most direct explanation by a Pentagon official amid criticism from opposition Republicans that the Democratic commander in chief is beating a hasty and risky retreat.

On Feb. 11, the White House said Ghani had requested “some flexibility in the troop drawdown timeline” and that the administration was “actively considering” that. A day later, Gen. John Campbell, the top U.S. commander in Afghanistan, told the U.S. Senate Armed Services Committee that he had presented U.S. leaders with several options that would allow him to better continue training and advising Afghan forces, particularly through this summer’s peak fighting season.

The “common denominator” in the new thinking about the U.S. military mission is a belief in Washington that the formation of a unity government in Kabul last year has opened new possibilities for progress on both the political and security fronts, Carter said.

The unity government of Ashraf and Chief Executive Abdullah Abdullah offers new promise for a more effective partnership in stabilizing the country, Carter said.

U.S. officials had grown grew impatient with former President Hamid Karzai, who sometimes publicly criticized the U.S. military and took a dimmer view of partnering with the Americans.

“That’s a major change,” Carter said, something “that just a few months ago we couldn’t have planned on.”

Obama’s current plan calls for troop levels to drop by half from 10,000 by the end of this year and be at nearly zero by the end of 2016. The U.S. would maintain a security cooperation office in Kabul. Ghani has made it known he thinks that should be slowed down in order to better support Afghan forces battling a resilient Taliban insurgency.

Carter did not describe in detail what changes Obama is considering in the U.S. military presence. But he said could include slowing the withdrawal pace and changing the timing and sequencing of U.S. base closures.

He said Obama also was “rethinking the details” of the U.S. counterterrorism mission in Afghanistan, where there are remnants of al-Qaida as well as signs that the Islamic State militant group is seeking to make inroads here in addition to Iraq and Syria.

In his remarks to reporters, Ghani thanked Obama for being flexible and showing a willingness to consider “the realities on the ground.” Using similar phrasing, Carter said that when he returns to Washington he will work up recommendations to Obama, in advance of the March talks, that “reflect reality on the ground.”

Carter lauded the progress that Afghanistan has made during the 13 years since U.S. forces invaded and toppled the Taliban rule. Obama’s goal, he said, is to “make sure this progress sticks” so that Afghanistan does not again become a launching pad for terrorist attacks on the U.S.

Carter also met in the Afghan capital with Campbell and Gen. Lloyd Austin, the commander of U.S. Central Command, which has responsibility for U.S. operations in Afghanistan and across the Middle East.